How do I deploy custom (in-house) Chromium Edge extensions to my organization?

Andrew Colombino - If you do not want to publish your extension to store (as hidden as well), the other option is to host the extension in a location within your network that is accessible to all users' devices & use the extension install source policy (which allows you to set the network location from where the extension can be picked up) along with force install policy to deploy the extension.

Here is the policy documentation for your reference:
Extension install sources - https://docs.microsoft.com/en-us/DeployEdge/microsoft-edge-policies#extensioninstallsources

Force install policy - https://docs.microsoft.com/en-us/DeployEdge/microsoft-edge-policies#extensioninstallforcelist

Let us know if you have any other questions!

Thanks!